F(40)=x^2-6x

Solution for F(40)=x^2-6x equation:

(40)=F^2-6F

We move all terms to the left:

(40)-(F^2-6F)=0

We get rid of parentheses

-F^2+6F+40=0

We add all the numbers together, and all the variables

-1F^2+6F+40=0

a = -1; b = 6; c = +40;
Δ = b2-4ac
Δ = 62-4·(-1)·40
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-1}=\frac{-20}{-2}
=+10
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-1}=\frac{8}{-2}
=-4
$